Design and optimization of TS firefly algorithm based on the nonhomogeneous linear polygonal T‐S fuzzy system

Wang, Guijun; Chen, Xue; Sun, Gang

doi:10.1002/int.22316

Cited by 1 publication

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References 27 publications

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“…See [25]. In 2021, Wang and Chen [26] further established the neural network model of the T-S fuzzy system by using the ordered representation of n-PFNs, and proposed the TS firefly algorithm of non-homogeneous linear polygonal T-S fuzzy system based on the flight characteristics of fireflies. See [27][28][29][30].…”

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confidence: 99%

Convergence and gradient algorithm of a class of neural networks based on the polygonal fuzzy numbers representation

Sun

Wang

2022

Complex Intell. Syst.

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As a special case of general fuzzy numbers, the polygonal fuzzy number can describe a fuzzy object by means of an ordered representation of finite real numbers. Different from general fuzzy numbers, the polygonal fuzzy numbers overcome the shortcoming of complex operations based on Zadeh’s traditional expansion principle, and can maintain the closeness of arithmetic operation. Hence, it is feasible to use a polygonal fuzzy number to approximate a general fuzzy number. First, an extension theorem of continuous functions on a real compact set is given according to open set construction theorem. Then using Weierstrass approximation theorem and ordered representation of the polygonal fuzzy numbers, the convergence of a single hidden layer feedforward polygonal fuzzy neural network is proved. Secondly, the gradient vector of the approximation error function and the optimization parameter vector of the network are given by using the ordered representation of polygonal fuzzy numbers, and then the gradient descent algorithm is used to train the optimal parameters of the polygonal fuzzy neural network iteratively. Finally, two simulation examples are given to verify the approximation ability of the network. Simulation result shows that the proposed network and the gradient descent algorithm are effective, and the single hidden layer feedforward network have good abilities in learning and generalization.

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